21x^2-2=x

Solution for 21x^2-2=x equation:

21x^2-2=x

We move all terms to the left:

21x^2-2-(x)=0

We add all the numbers together, and all the variables

21x^2-1x-2=0

a = 21; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·21·(-2)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-13}{2*21}=\frac{-12}{42}
=-2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+13}{2*21}=\frac{14}{42}
=1/3
$